新版GRE数学复习重要考点：At Least Once

If probability of an event happening is p, then the probability that the event happens at least once in n trials is 1-(1-p)^∧n.

Example:

To understand the equation follow these steps:

1.The probability of the event not happening is 1-p.

2.The probability it won't happen n-times in a row is (1-p)^∧n.

3.Probability it will happen at least once is 1-(1-p)^∧n.

Probability that a roll of a six-sided die land with face 1 is 1/6.Then the probability that 1 will turn up at least once in 3 tries:=1-(1-1/6)^∧3=1-(5/6)^∧3.

Remember:

It is much harder to directly calculate the at-least-once probability.